It's set up so that when the free trial ends, you are automatically rolled over into a subscription, which would require the payment details.
You have 7 days to decide if you want to keep or cancel the subscription, and there is a 14-day grace period once the subscription starts in which you can still cancel. I'd advise cancelling as soon as possible if you decide the program isn't what you want.
If you have issues canceling the subscription, contact customer support immediately to avoid cancellation fees. Be sure to read the subscription terms linked to on the payment information page, as they describe things such as automatic rollover of subscriptions and fees for early contract cancellation: https://www.adobe.com/legal/subscription-terms.html
All merchants these days must ensure the bank/credit card is good before they accept it toward subscription payment. The way they do that is by submitting a nominal charge (usually under 1 dollar/euro) to verify the card is not stolen. The fee is then credited back to your subscription account. If you're not seriously interested in using the software/service, do not take out the trial.